# Joan is on summer break and spends most of her time either playing video games or browsing the internet. Her utility function is U(q1; q2) = 3q0:2 1…

Joan is on summer break and spends most of her time either playing video games

or browsing the internet. Her utility function is U(q1; q2) = 3q0:2

1 q0:8

2 , where q1 represents the

hours spent browsing the internet and q2 hours playing video games. Joan does not have a budget

constraint but she has 15 hours to spend on both activities.

(a) (5 points) Write the equation for one of Joan’s indifference curves when the level of utility is

equal to 100.

(b) (5 points) Write Joan’s time constraint.

(c) (10 points) Find the amount of hours that Joan will spend on each activity that maximizes her

utility and satisfies her time constraint. Use either the substitution or Lagrangian method.

(d) (5 points) Can Joan afford any bundle that yields a utility of 50? Explain.

(e) (5 points) How does Joan’s optimum amount of time spent on each activity change if her

utility function is U(q1; q2) = 5ln(3) + ln(q1) + 4ln(q2)?